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Question
Find the coefficients of x60 in the expansion of `(1/x^2 + x^4)^18`
Solution
Here a = `1/x^2`, b = x4, n = 18
We have, tr+1 = nCr an–r .br
= `""^18"C"_"r"(1/(x^2))^(18-"r") (x^4)^"r"`
= 18Cr x2r–36 .x4r
= 18Cr x6r–36
To get the coefficient of x60, we must have
x6r–36 = x60
∴ 6r – 36 = 60
∴ 6r = 96
∴ r = 16
∴ Coefficient of x60
= 18C16
= `(18!)/(16!2!)`
= `(18 xx 17 xx 16!)/(16! xx 2 xx 1)`
= 153
∴ the coefficient of x60 is 153
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